Modern Observational/Instrumentation Techniques Astronomy 500sheinis/ast500/AY500_lect4.ppt.pdf · •Integrated light from unresolved extended sources •Thermal emission from dust

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ModernObservational/Instrumentation

TechniquesAstronomy 500

Andy Sheinis, Sterling 5520,2-0492sheinis@astro.wisc.eduMW 2:30, 6515 SterlingOffice Hours: Tu 11-12

Coherent vs Incoherent•Radio, Microwave, Sub-mm•Single-mode optics•Wave Statistics•Time-domainspectroscopy

•Sub-mm,IR, optical, UV,x-ray, gamma-ray•Multi-mode optics•Poisson Statistics•Dispersive or energy-resolved spectroscopy

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Spatially resolved?

• Point source– we are measuring flux– E=Afνdt

• Resolved source– We are measuring surface brightness– E=AΩIν

Signal-to-Noise (S/N)

• Signal=R*• t time

detected e-/second

• Consider the case where we count all the detected e- in a circular aperture with radius r.

I

sky

r

r

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• Noise Sources:

!

R* " t # shot noise from source

Rsky " t " $r2 # shot noise from sky in aperture

RN2" $r2 # readout noise in aperture

RN2 + (0.5 % gain)2[ ] " $r2 # more general RN

Dark " t " $r2 # shot noise in dark current in aperture

R* = e&/sec from the source

Rsky = e&/sec/pixel from the sky

RN = read noise (as if RN2 e& had been detected)

Dark = e_ /second/pixel

Sources of Background noise•Relic Radiation from Big Bang•Integrated light from unresolved extended sources•Thermal emission from dust•Starlight scattered from dust•Solar light scattered from dust (ZL)•Line emission from galactic Nebulae•Line emission from upper atmosphere (Airglow)•Thermal from atmosphere•Sun/moonlight scattered by atmosphere•Manmade light scattered into the beam•Thermal or scatter from the telescope/dome/instrument

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S/N for object measured in aperture with radius r: npix=#of pixels in the aperture= πr2

!

R*t

R* " t + Rsky " t " npix + RN +gain

2

#

$ %

&

' ( 2

" npix +Dark " t " npix)

* +

,

- .

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2

Signal

Noise

!

(R*" t)

2

All the noise terms added in quadratureNote: always calculate in e-

Noise from sky e- in aperture

Noise from the darkcurrent in aperture

Readnoise in aperture

What is ignored in this S/Neqn?

• Bias level/structure correction• Flat-fielding errors• Charge Transfer Efficiency (CTE)

0.99999/pixel transfer• Non-linearity when approaching full well• Scale changes in focal plane• A zillion other potential problems

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S/N Calculations

• So, what do you do with this?– Demonstrate feasibility– Justify observing time requests– Get your observations right– Estimate limiting magnitudes for existing or

new instruments– Discover problems with instruments,

telescopes or observations

How do you get values forsome of these parameters?

• Dark Current: CCD@-120˚C < 2e-/pix/hour Insb: ~2e-/pix/sec• RN: CCD: 2 - 6 e-/pix Insb: 10 - 25 e-/pix• R*: for a given source brightness, this can be

calculated for any telescope and total systemefficiency.

• In practice: Go to the facility WWW site foreverything!

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Source Count Rates

Example: LRIS on Keck 1 for a B=V=R=I=20mag object @ airmass=1

1367 e-/secI1890 e-/secR1521 e-/secV1470 e-/secB To calculate R* for a source of

arbitrary brightness onlyrequires this table and a bit ofmagnitude math.

Source Count Rates

!

m1 = co" 2.5log(I1).............................(1)

m2 = co" 2.5log(I2)............................(2)

m1 "m2 = "2.5 log(I1) " log(I2)[ ].........(1) " (2)

m1 "m2 = "2.5log I1I2( )

I1

I2=10

"m1"m22.5( )

I1 = R*(m1) = I20 #10"

m1"20

2.5

$ % &

' ( )

Let I2 be the intensity for the fiducial m=20 object

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RskySignal from the sky background ispresent in every pixel of theaperture. Because each instrumentgenerally has a different pixel scale,the sky brightness is usuallytabulated for a site in units ofmag/arcsecond2.

˝(mag/ )

19.219.920.019.517.014

19.520.320.720.718.510

19.720.621.421.619.97

19.920.821.722.421.53

19.920.921.822.722.00

IRVBULunarage

(days)

NaD OH

Hg

!

Scale""/pix (LRIS - R : 0.218"/pix)

Area of 1 pixel = (Scale)2 (LRIS#R : 0.0475"2

this is the ratio of flux/pix to flux/"

In magnitudes :

Ipix = I"Scale2 I" Intensity (e-/sec)

#2.5log(Ipix ) = #2.5[log(I") + log(Scale2)]

mpix = m"# 2.5log(Scale2) (for LRIS - R : add 3.303mag)

and

Rsky (mpix ) = R(m = 20) $10(0.4#m pix )

Example, LRIS in the R - band :

Rsky =1890 $100.4(20#24.21)= 39.1 e- /pix /sec

R sky = 6.35e- /pix /sec % RN in just 1 second

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S/N - some limiting cases. Let’s assume CCD withDark=0, well sampled read noise.

!

R*t

R* " t + Rsky " t " npix + RN( )2" npix[ ]

1

2

Bright Sources: (R*t)1/2 dominates noise term

!

S/N "R*t

R*t

= R*t # t

1

2

Sky Limited

!

( Rskyt > 3"RN) : S/N#R*t

npixRskyt# t

Note: seeing comes in with npix term

Read-noise Limited

!

(3 Rskyt < RN) : S/N"R*t

npixRN2" t

S/N ~ # of exposures

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http://www.gemini.edu/sciops/ObsProcess/obsConstraints/ocTransparency.html

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Writing Proposals

• First and foremost: Scientific Justification!– Give context– Clearly state what unanswered questions are to be

addressed– Clearly state what you will do new or better

• Look Competent and Smart– Do S/N and exposure time calculations– Defend choice of filters/spectral resolution sample size etc.

Observing

• Rule #1 -- keep collecting photons!• Know your S/N targets• Plan the night out carefully ahead of

time• Useful tools:

– Aircharts

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• Right Ascension (RA) andDeclination (Dec) are equatorial skycoordinates

• Like longitude and latitude(respectively) on the surface of theEarth but fixed on the sky

• Aligned with the Earth’s axis so theRA and Dec for celestial objectschanges as the Earth’s orbitprecesses. Need to specify the“epoch” of the coordinates.

Hour angles and airmass• The sidereal time gives the

right ascension that ispassing through themeridian. Index point isVernal equinox, 12h isoverhead at local midnight onMarch 21. Sky advances 2hours per month.

• The hour angle is the timebefore or after a particularRA is at the meridian.HA=LST-RA

• Airmass is a combination ofthe HA and the differencebetween the telescopelatitude and the pointingdeclination.Airmass~sec(zenith angle)

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• IRAF Airchart in the mtools packages is very handy.• Typically observe with airmass=X<2• Atmospheric dispersion can be a problem for X>1.5• http://www.eso.org/observing/bin/skycalcw/airmass

There are oftenother limits thatgovern where youcan point in the sky.

East

North

1h2h

3h

Dec=-30